Hidden crossing theory of charge exchange in H + + He + (1 s ) collisions in vicinity of maximum of cross section

Within the framework of dynamical adiabatic approach the hidden crossing theory of inelastic transitions is applied to charge exchange in H+ + He+ (1s ) collisions in the wide range of center of mass collision energies E cm = (1.6– 70) keV. The good agreement with experiment and molecular close coupling calculations is obtained. At low energies our 4-state results are closest to the experiment and correctly reproduce the shoulder in energy dependence of the cross section around E cm = 6 keV. The 2-state results correctly predict the position of the maximum of the cross section at E cm ≈ 40 keV, whereas 4-state results fail to correctly describe the region around the maximum. The reason for this is the fact that adiabatic approximation for a given two-state hidden crossing is applicable for values of the Schtueckelberg parameter >1. But with increase of principal quantum number N the Schtueckelberg parameter decreases as ~N −3 . That is why the 4-state approach involving higher excited states fails at smaller collision energies E cm ≈ 15 keV, while the 2-state approximation which involves low lying states can be extended to higher collision energies.